You measure two quantities as A = 1.0 m ± 0.2 m, B = 2.0 m ± 0.2 m. We should report the correct value for √AB as: a) 1.4 m ± 0.4 m b) 1.41 m ± 0.15 m c) 1.4 m ± 0.3 m d) 1.4 m ± 0.2 m
Here, A=1.0m±0.2m, B=2.0m±0.2m AB=(1.0m)(2.0m)=2.0m2 AB=2.0m=1.414m Rounding off to two significant figures, we get AB=1.4m ABΔAB=21(AΔA+BΔB)=21(1.00.2+2.00.2)=20.3 ΔAB=20.3×AB=20.3×1.414=0.212m Rounding off to one significant figure, we get ΔAB=0.2m The correct value for AB is 1.4m±0.2m.
